Posts tagged nonparametric
Quantile Regression with BART
- 25 January 2023
Usually when doing regression we model the conditional mean of some distribution. Common cases are a Normal distribution for continuous unbounded responses, a Poisson distribution for count data, etc.
Modeling spatial point patterns with a marked log-Gaussian Cox process
- 31 May 2022
The log-Gaussian Cox process (LGCP) is a probabilistic model of point patterns typically observed in space or time. It has two main components. First, an underlying intensity field \(\lambda(s)\) of positive real values is modeled over the entire domain \(X\) using an exponentially-transformed Gaussian process which constrains \(\lambda\) to be positive. Then, this intensity field is used to parameterize a Poisson point process which represents a stochastic mechanism for placing points in space. Some phenomena amenable to this representation include the incidence of cancer cases across a county, or the spatiotemporal locations of crime events in a city. Both spatial and temporal dimensions can be handled equivalently within this framework, though this tutorial only addresses data in two spatial dimensions.
Bayesian Additive Regression Trees: Introduction
- 21 December 2021
Bayesian additive regression trees (BART) is a non-parametric regression approach. If we have some covariates \(X\) and we want to use them to model \(Y\), a BART model (omitting the priors) can be represented as:
Student-t Process
- 21 August 2017
PyMC also includes T-process priors. They are a generalization of a Gaussian process prior to the multivariate Student’s T distribution. The usage is identical to that of gp.Latent, except they require a degrees of freedom parameter when they are specified in the model. For more information, see chapter 9 of Rasmussen+Williams, and Shah et al..